Journal article

Topological recursion with hard edges

Leonid Chekhov, Paul Norbury

INTERNATIONAL JOURNAL OF MATHEMATICS | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2019

Abstract

We prove a Givental type decomposition for partition functions that arise out of topological recursion applied to spectral curves. Copies of the Konstevich-Witten KdV tau function arise out of regular spectral curves and copies of the Brezin-Gross-Witten KdV tau function arise out of irregular spectral curves. We present the example of this decomposition for the matrix model with two hard edges and spectral curve (x 2 - 4)y 2 = 1.

University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Awarded by Russian Foundation for Basic Research


Awarded by ERC


Funding Acknowledgements

The authors would like to thank Maxim Kazarian, Nicolas Orantin, Sergey Shadrin and Peter Zograf for useful conversations and the referee for many useful comments. PN was partially supported by the Australian Research Council grants DP170102028 and DP180103891. The work of L. Ch. was partially supported by the Russian Foundation for Basic Research (Grant No. 17-01-00477) and by the ERC Advanced Grant 291092 "Exploring the Quantum Universe" (EQU).